The Shape of Data
Exploring how topology can extract new insights from abundant data, focusing on innovative applications of abstract mathematics to deepen our understanding of complex datasets.
The Story of Mathematical Proof - From Ancient Greece to Modern Logic
Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.
Cohomological Donaldson-Thomas Invariants of 3-Manifolds
Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
On Mapping Class Groups of Non-Orientable Surfaces
Exploración de la estructura y cohomología de grupos de clases de mapeo en superficies no orientables, incluyendo resultados recientes sobre el plano proyectivo y la botella de Klein.
Tangent Groupoid in Noncommutative Geometry - Lecture 20
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Mohammed Abouzaid: Bordism and Floer Theory
Explore the intersection of Morse theory and infinite-dimensional spaces in topology. Learn about recent advances in Floer theory and its applications to generalized homology and derived orbifold bordism.
A Local Torelli Theorem for Log Symplectic Manifolds
Explore log symplectic manifolds, their moduli space, and local Torelli theorem. Discover new components in Pn's moduli space of log symplectic structures.
Cohomological Obstructions to Group Stability
Explore cohomological obstructions to group stability in this advanced mathematics seminar, delving into operator algebras and their applications in group theory.
Tangent Groupoid in Noncommutative Geometry - Lecture 19
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Archimedes' Claw and Carousel - Upgrading Ancient Discoveries
Explore Archimedes' mathematical discoveries upgraded after 2000 years, including the baggage carousel concept, inside-out animations, and the fascinating Archimedes' claw.
Pumping Chirality in Three Dimensions - IPAM at UCLA
Explore quantum cellular automata, bosonization, and chirality pumping in 3D systems. Discover connections to quantum error correction and topological physics in this advanced physics lecture.
Tangent Groupoid in Noncommutative Geometry - Lecture 17
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Geodesic Complexity and Fibered Decompositions of Cut Loci
Explore geodesic complexity in Riemannian manifolds, focusing on cut locus structure and fibered decompositions to establish bounds and applications in projective and lens spaces.
Tangent Groupoid in Noncommutative Geometry - Lecture 18
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 21
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Homeomorphisms of Euclidean Space
Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.
Tangent Groupoid in Noncommutative Geometry - Lecture 11
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 9
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
A Sheaf-Theoretic Construction of Shape Space
Sheaf-theoretic approach to construct shape space using Persistent Homology Transform. Explores homotopy sheaves, metrics, stability theorems, and approximation of manifolds.
Tangent Groupoid in Noncommutative Geometry - Lecture 10
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 7
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.